IC1
On the Global Regularity of the Three-dimensional Navier-Stokes Equations and Other Relevant Geophysical Models

The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, the so-called the ``Primitive Equations'', is often prohibitively expensive computationally, and hard to study analytically. In this talk we will survey the main obstacles in proving the global regularity for the three-dimensional Navier--Stokes equations and their geophysical counterparts. Even though the Primitive Equations look as if they are more difficult to study analytically than the three-dimensional Navier--Stokes equations we will show in this talk that they have a unique global (in time) regular solution for all initial data.